Damping: Three Basic Questions

Hello All,

I have some basic damping related questions that I am hoping you all can shed some light on or suggest some resources on to someone who has taken a few undergraduate level physics courses.

i.) Can someone give me an intuitive explanation as to why linear damping (underdamped case) of a harmonic oscillator shortens the period?

ii.) Must an oscillatory system with any kind of damping (including nonlinear damping) have a shorter period/higher frequency than the undamped system?

iii.) Why does damping cause a broader peak in the power spectrum of the oscillatory time series (please try to give me an intuitive reason not a purely mathematical one)?


Thank you in advance


-Mudbone